Publications [#354026] of Hongkai Zhao

Papers Published

1. Zhao, H; Bryson, J; Vershynin, R, Marchenko-Pastur law with relaxed independence conditions, Random Matrices: Theory and Applications (2021), World Scientific Publishing [doi]
   (last updated on 2024/04/17)

   Abstract:
   We prove the Marchenko–Pastur law for the eigenvalues of p × p sample covariance matrices in two new situations where the data does not have independent coordinates. In the first scenario — the block-independent model — the p coordinates of the data are partitioned into blocks in such a way that the entries in different blocks are independent, but the entries from the same block may be dependent. In the second scenario — the random tensor model — the data is the homogeneous random tensor of order d, i.e. the coordinates of the data are all (nd) different products of d variables chosen from a set of n independent random variables. We show that Marchenko–Pastur law holds for the block-independent model as long as the size of the largest block is o(p), and for the random tensor model as long as d = o(n1/3). Our main technical tools are new concentration inequalities for quadratic forms in random variables with block-independent coordinates, and for random tensors.